Gravitational Wave Detection Using Pulsar Timing Current Status and Future Progress Fredrick A. Jenet Center for Gravitational Wave Astronomy University of Texas at Brownsville

Collaborators Dick Manchester ATNF/CSIRO Australia George Hobbs ATNF/CSIRO Australia KJ Lee Peking U. China Andrea Lommen Franklin & Marshall USA Shane L. Larson Penn State USA Linqing Wen AEI Germany Teviet Creighton Caltech USA John Armstrong JPL USA

Main Points Radio pulsar can directly detect gravitational waves –How can you do that? What can we learn? –Astrophysics –Gravity Current State of affairs What can the SKA do.

Radio Pulsars

Gravitational Waves “Ripples in the fabric of space-time itself” g  =   + h    h  /   t +  2 h  = 4  T  G  (g) = 8  T 

Three Categories of G-waves Periodic Signals (Single Source) Burst Signals (Single Source) Stochastic Signals (Multiple Sources)

Pulsar Timing Pulsar timing is the act of measuring the arrival times of the individual pulses

How does one detect G- waves using Radio pulsars? Pulsar timing involves measuring the time-of arrival (TOA) of each individual pulse and then subtracting off the expected time-of-arrival given a physical model of the system. R = TOA – TOA m

Timing residuals from PSR B From Jenet, Lommen, Larson, & Wen, ApJ, May, 2004 Data from Kaspi et al Period =5.36 ms Orbital Period =12.32 days

The effect of G-waves on pulsar timing Earth Pulsar

kk  Photon Path G-wave Pulsar Earth

t0 t0 + P0 t0 + P0 + P1 t0 + P0 + P1 + P2 TOA(N) =  0 N-1 P i + t 0 P i = P i m +  P i R(N) = TOA(N) – TOA(N) m =  0 N-1  P i P i = 1/ i = 1/( i m +  i ) R(N) = -  0 N-1  i /( i m ) 2 R(t) = -  0 N-1 P i m  i / v i m

The effect of G-waves on the Timing residuals

h =  RR rms  1  sh >= 1  s  /N 1/  h Frequency, Hz 3     Sensitivity of a Pulsar timing “Detector” * 3C 66B M sun a distance of 20 Mpc 10 9 M sun a distance of 20 Mpc SMBH Background * OJ287

Detection vs Limits A single pulsar can place limits on the existence of G-waves Plot thanks to George Hobbs

The Stochastic Background h c (f) = A f   gw (f) = (2  2 /3 H 0 2 ) f 2 h c (f) 2 Super-massive Black Holes:  = -2/3 A = yrs -2/3 Characterized by its “Characterictic Strain” Spectrum: Jaffe & Backer (2002) Wyithe & Lobe (2002) Enoki, Inoue, Nagashima, Sugiyama (2004) For Cosmic Strings:  = -7/6 A= yrs -7/6 Damour & Vilenkin (2005)

The Stochastic Background The best limits on the background are due to pulsar timing. For the case where  gw (f) is assumed to be a constant (  =-1): Kaspi et al (1994) report  gw h 2 < 6  (95% confidence) McHugh et al. (1996) report  gw h 2 < 9.3  Frequentist Analysis using Monte-Carlo simulations Yield  gw h 2 < 1.2  10 -7

The Stochastic Background The Parkes Pulsar Timing Array Project Goal: Time 20 pulsars with 100 nano-second residual RMS over 5 years Current Status Timing 20 pulsars for 2 years, 5 currently have an RMS < 300 ns Combining this data with the Kaspi et al data yields:  = -1 : A<4  yrs - 1  gw h 2 < 8.8   = -2/3 : A<6.5  yrs -2/3  gw (1/20 yrs)h 2 < 3.0   = -7/6 : A<2.2  yrs -7/6  gw (1/20 yrs)h 2 < 6.9  10 -9

The Stochastic Background With the SKA: 40 pulsars, 10 ns RMS, 10 years  = -1 : A<3.6   gw h 2 < 6.8   = -2/3 : A<6.0   gw (1/10 yrs)h^2 < 4.0   = -7/6 : A<2.0   gw (1/10 yrs)h^2 < 2.1 

The Stochastic Background A Dream, or almost reality with SKA: 40 pulsars, 1 ns RMS, 20 years  = -2/3 : A<1.0   gw (1/10 yrs)h^2 < 1.0  The expected background due to white dwarf binaries lies in the range of A = ! (Phinney (2001)) Individual 10 8 solar mass black hole binaries out to ~100 Mpc. Individual 10 9 solar mass black hole binaries out to ~1 Gpc

The timing residuals for a stochastic background This is the same for all pulsars. This depends on the pulsar. The induced residuals for different pulsars will be correlated.

Two-point correlation Two basic techniques Spherical Harmonic Decomposition Hellings & Downs 1983 Jenet, Hobbs, Lee, & Manchester 2005 Jaffe & Backer 2002

The Expected Correlation Function Assuming the G-wave background is isotropic:

The Expected Correlation Function

How to detect the Background For a set of N p pulsars, calculate all the possible correlations:

How to detect the Background

Search for the presence of  (  ) in C(  ):

How to detect the Background The expected value of  is given by: In the absence of a correlation,  will be Gaussianly distributed with:

How to detect the Background The significance of a measured correlation is given by:

Single Pulsar Limit (1  s, 7 years) Expected Regime For a background of SMBH binaries: h c = A f -2/3 20 pulsars.

Single Pulsar Limit (1  s, 7 years) 1  s, 1 year Expected Regime For a background of SMBH binaries: h c = A f -2/3 20 pulsars.

Single Pulsar Limit (1  s, 7 years) 1  s, 1 year (Current ability) Expected Regime.1  s 5 years For a background of SMBH binaries: h c = A f -2/3 20 pulsars.

Single Pulsar Limit (1  s, 7 years) 1  s, 1 year (Current ability) Expected Regime.1  s 5 years.1  s 10 years For a background of SMBH binaries: h c = A f -2/3 20 pulsars.

Single Pulsar Limit (1  s, 7 years) 1  s, 1 year (Current ability) Expected Regime.1  s 5 years.1  s 10 years SKA 10 ns 5 years 40 pulsars h c = A f -2/3 Detection SNR for a given level of the SMBH background Using 20 pulsars

Graviton Mass Current solar system limits place m g < eV  2 = k 2 + (2  m g /h) 2 c = 1/ (4 months) Detecting 5 year period G-waves reduces the upper bound on the graviton mass by a factor of 15. By comparing E&M and G-wave measurements, LISA is expected to make a 3-5 times improvement using LMXRB’s and perhaps up to 10 times better using Helium Cataclismic Variables. (Cutler et al. 2002)

Radio pulsars can directly detect gravitational waves –R = h/  s, 100 ns (current), 10 ns (SKA) What can we learn? –Is GR correct? SKA will allow a high SNR measurement of the residual correlation function -> Test polarization properties of G-waves Detection implies best limit of Graviton Mass (15-30 x) –The spectrum of the background set by the astrophysics of the source. For SMBHs : Rate, Mass, Distribution (Help LISA?) Current Limits –For SMBH, A<6.5  or  gw (1/20 yrs)h 2 < 3.0  SKA Limits –For SMBH, A<6.0  or  gw (1/10 yrs)h 2 < 4.0  –Dreamland: A<1.0  or  gw (1/10 yrs)h 2 < 1.0  Individual 10 8 solar mass black hole binaries out to ~100 Mpc. Individual 10 9 solar mass black hole binaries out to ~1 Gpc